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Substitute Numbers for Letters in Simple Sums

In this worksheet, students will replace letters with numbers and carry out simple questions using the four number operations. (The student will type the answer as a number and no prioritisation of calculations is required at this stage.)

Worksheet Overview

QUESTION 1 of 10

Make sure that you’ve got your thinking cap on as we are going to be number decoders!

In this activity, we are going to swap numbers for letters to solve maths problems.

Let’s take a look at this question first:

If a = 1, b = 2, c = 3 and d = 4, what is c x d?

This is called algebra, which is where numbers are replaced with letters. We need to swap the letters back into numbers to solve this problem.

If we put the numbers back in, then c x d becomes 3 x 4. We know this is 12.

The values of the letters can be different in each question.

Let’s try this question next:

If a = 7, b = 4, c = 8 and p = 3, what is a +b + c?

Let’s swap the letters back to numbers. This would be written as: 7 + 4 + 8 = 19.

Remember, when you are adding lots of numbers, you can choose the order that you add them in.

If there is a mixture of addition and subtraction, you must work it out in the order that it is written.

Let’s practise this now:

If a = 10, b = 4, c = 3 and d = 9, what is b + d - a + c?

Let’s swap the letters back to numbers. This would be written as: 4 + 9 - 10 + 3 =

Remember, we must answer this one in order.

So 4 + 9 = 13…

13 - 10 = 3…

3 + 3 = 6.

Now it’s your turn to crack the codes. Good luck number detective!

Let's begin by practicing converting between letters and numbers.

If a = 1, b = 2, c = 3 and d = 4, what is c + d?

Which is the correct sum from the options below?

1 + 2

3 + 4

3 + 2

4 + 1

Now let's take the next step to reaching the answer.

What is 3 + 4?

If A = 3, B = 4, C = 5 and D = 6, what is D - B?

Which is the correct sum from the options below?

6 - 5

5 - 3

6 - 4

6 - 3

Now let's take the next step to reaching the answer.

What is 6 - 4?

If A = 7, B = 5, C = 3 and D = 2, which letters have been used to make the sum 5 + 3?

Which is the correct sum from the options below?

B + C

A + D

B + A

B + D

If A = 7, B = 5, C = 3 and D = 2, what is B + C?

If a = 10, b = 12, c = 7 and d = 8, which letters have been used to make the sum 10 + 7?

Which is the correct sum from the options below?

b + c

a + c

b + a

b + d

If A = 10, B = 12, C = 7 and D = 8, what is A + C?

If A = 3, B = 17, C = 15 and D = 9, which letters have been used in the sum if the answer is 12?

Which is the correct sum from the options below?

B - C

D + A

B + A

B - D

If a = 3, b = 7, c = 15 and d = 9, which letters have been used in the sum if the answer is 10?

Which is the correct sum from the options below?

c - b

d + a

b + a

d - b

ANSWERS

Question 1

Let's begin by practicing converting between letters and numbers.

If a = 1, b = 2, c = 3 and d = 4, what is c + d?

Which is the correct sum from the options below?

CORRECT ANSWER

3 + 4

EDDIE SAYS

We are told in the question that c = 3 and d = 4.
If we swap the letters for the numbers they represent, the correct sum must be 3 + 4.

ANSWERS

Question 2

Now let's take the next step to reaching the answer.

What is 3 + 4?

CORRECT ANSWER

7

EDDIE SAYS

Following on from the previous question, we now need to add 3 and 4.
3 + 4 = 7
So the answer to c + d = 7.

ANSWERS

Question 3

If A = 3, B = 4, C = 5 and D = 6, what is D - B?

Which is the correct sum from the options below?

CORRECT ANSWER

6 - 4

EDDIE SAYS

We are told in the question that D = 6 and B = 4.
If we swap the letters for the numbers they represent, the correct sum must be 6 - 4.
Remember that the letter values will often change in each question, so be careful not to fall into that sneaky trap!

ANSWERS

Question 4

Now let's take the next step to reaching the answer.

What is 6 - 4?

CORRECT ANSWER

2

EDDIE SAYS

Following on from the previous question, we now need to take away 4 from 6.
6 - 4 = 2
So the answer to B - D = 2.

ANSWERS

Question 5

If A = 7, B = 5, C = 3 and D = 2, which letters have been used to make the sum 5 + 3?

Which is the correct sum from the options below?

CORRECT ANSWER

B + C

EDDIE SAYS

We are told in the question that B = 5 and C = 3.
If we swap these letters in for the numbers, the correct sum must be B + C.

ANSWERS

Question 6

If A = 7, B = 5, C = 3 and D = 2, what is B + C?

CORRECT ANSWER

8

EDDIE SAYS

We are told in the question that B = 5 and C = 3.
If we swap the numbers in the place of the letters they represent, the sum to be calculated is 5 + 3.
5 + 3 = 8.

ANSWERS

Question 7

If a = 10, b = 12, c = 7 and d = 8, which letters have been used to make the sum 10 + 7?

Which is the correct sum from the options below?

CORRECT ANSWER

a + c

EDDIE SAYS

We are told in the question that a = 10 and c = 7.
If we swap the letters in for the numbers they represent, the correct sum must be a + c.

ANSWERS

Question 8

If A = 10, B = 12, C = 7 and D = 8, what is A + C?

CORRECT ANSWER

17

EDDIE SAYS

We are told in the question that A = 10 and C = 7.
If we swap the numbers in the place of the letters they represent, the sum to be calculated is 10 + 7.
10 + 7 = 17.

ANSWERS

Question 9

If A = 3, B = 17, C = 15 and D = 9, which letters have been used in the sum if the answer is 12?

Which is the correct sum from the options below?

CORRECT ANSWER

D + A

EDDIE SAYS

We know we are looking for an answer of 12, so we need to work out which of these sums gives this answer.
B - C > 17 - 15 = 2, which is not the answer we need.
D + A > 9 + 3 = 12, this is what we are looking for! But let's check the others just in case.
B + A > 17 + 3 = 20, which is not the answer we need.
B - D > 17 - 9 = 8, which is not the answer we need.
So D + A is the only sum which gives is an answer of 12, so this is the correct answer.

ANSWERS

Question 10

If a = 3, b = 7, c = 15 and d = 9, which letters have been used in the sum if the answer is 10?

Which is the correct sum from the options below?

CORRECT ANSWER

b + a

EDDIE SAYS

We know we are looking for an answer of 10, so we need to work out which of these sums gives this answer.
c - b > 15 - 7 = 8, which is not the answer we need.
d + a > 9 + 3 = 12, which is not the answer we need.
b + a > 7 + 3 = 10, this is what we are looking for! But let's check the last option just in case.
d - b > 9 - 7 = 2, which is not the answer we need.
So b + a is the only sum which gives is an answer of 10, so this is the correct answer.

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